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ComparingNetPresentValueandInternalRateofReturn1of5•Netpresentvalue(NPV)andinternalrateofreturn(IRR)aretwoverypracticaldiscountedcashflow(DCF)calculationsusedformakingcapitalbudgetingdecisions.•NPVandIRRleadtothesamedecisionswithinvestmentsthatareindependent.•Withmutuallyexclusiveinvestments,theNPVmethodiseasiertouseandmorereliable.IntroductionTothispointneitherofthetwodiscountedcashflowproceduresforevaluatinganinvestmentisobviouslyincorrect.Inmanysituations,theinternalrateofreturn(IRR)procedurewillleadtothesamedecisionasthenetpresentvalue(NPV)procedure,buttherearealsotimeswhentheIRRmayleadtodifferentdecisionsfromthoseobtainedbyusingthenetpresentvalueprocedure.Whenthetwomethodsleadtodifferentdecisions,thenetpresentvaluemethodtendstogivebetterdecisions.ItissometimespossibletousetheIRRmethodinsuchawaythatitgivesthesameresultsastheNPVmethod.Forthistooccur,itisnecessarythattherateofdiscountatwhichitisappropriatetodiscountfuturecashproceedsbethesameforallfutureyears.Iftheappropriaterateofinterestvariesfromyeartoyear,thenthetwoproceduresmaynotgiveidenticalanswers.ItiseasytousetheNPVmethodcorrectly.ItismuchmoredifficulttousetheIRRmethodcorrectly.AcceptorRejectDecisionsFrequently,theinvestmentdecisiontobemadeiswhethertoacceptorrejectaprojectwherethecashflowsoftheprojectdonotaffectthecashflowsofotherprojects.Wespeakofthistypeofinvestmentasbeinganindependentinvestment.WiththeIRRprocedure,therecommendationwithconventionalcashflowsistoacceptanindependentinvestmentifitsIRRisgreaterthansomeminimumacceptablerateofdiscount.Ifthecashflowcorrespondingtotheinvestmentconsistsofoneormoreperiodsofcashoutlaysfollowedonlybyperiodsofcashproceeds,thismethodwillgivethesameacceptorrejectdecisionsastheNPVmethod,usingthesamediscountrate.Becausemostindependentinvestmentshavecashflowpatternsthatmeetthespecificationsdescribed,itisfairtosaythatinpractice,theIRRandNPVmethodstendtogivethesameacceptorrejectrecommendationsforindependentinvestments.MutuallyExclusiveInvestmentIfundertakinganyoneofasetofinvestmentswillchangetheprofitabilityoftheotherinvestments,theinvestmentsaresubstitutes.Anextremecaseofsubstitutionexistsifundertakingoneoftheinvestmentscompletelyeliminatestheexpectedproceedsoftheotherinvestments.Suchinvestmentsaresaidtobemutuallyexclusive.Frequently,acompanywillhavetwoormoreinvestments,anyoneofwhichwouldbeacceptable,butbecausetheinvestmentsaremutuallyexclusive,onlyonecanbeaccepted.Mutuallyexclusiveinvestmentalternativesarecommoninindustry.Thesituationfrequentlyoccursinconnectionwiththeengineeringdesignofanewinstallation.Intheprocessofdesigningsuchaninstallation,theengineersaretypicallyfacedatagreatmanypointswithalternativesthataremutuallyexclusive.Thus,ameasureofinvestmentworththatdoesnotleadtocorrectmutuallyexclusivechoiceswillbeseriouslydeficient.ComparingNetPresentValueandInternalRateofReturn2of5’srecommendationsformutuallyexclusiveinvestmentsarelessreliablethanarethosethatresultfromtheapplicationoftheNPVmethodbecausetheformerfailtoconsiderthesizeoftheinvestment.Letusassumethatwemustchooseoneofthefollowinginvestmentsforacompanywhosediscountrateis10%:InvestmentArequiresanoutlayof$10,000thisyearandhascashproceedsof$12,000nextyear;investmentBrequiresanoutlayof$15,000thisyearandhascashproceedsof$17,700nextyear.TheIRRofAis20%,andthatofBis18%.AquickanswerwouldbethatAismoredesirable,basedonthehypothesisthatthehighertheIRR,thebettertheinvestment.WhenonlytheIRRoftheinvestmentisconsidered,somethingsignificantisleftout¾andthatisthesizeoftheinvestment.TheimportantdifferencebetweeninvestmentsBandAisthatBrequiresanadditionaloutlayof$5,000andprovidesadditionalcashproceedsof$5,700.Table1showsthattheIRRoftheincrementalinvestmentis14%,whichisclearlyworthwhileforacompanythatcanobtainadditionalfundsat10%.The$5,000savedbyinvestinginAcanearn$5,500(a10%return).Thisisinferiortothe$5,700earnedbyinvestinganadditional$5,000inB.Table1.Twomutuallyexclusiveinvestments,AandBCashflowsInvestment01IRR(%)A#$10,000$12,00020B#15,00017,70018Incremental(B#A)#$5,000+$5,00014Figure1.Twomutuallyexclusiveinvestments,AandBComparingNetPresentValueandInternalRateofReturn3of5(hasahigherpresentvalue)aslongasthediscountrateislessthan14%.WecanidentifythedifficultyjustdescribedasthescaleorsizeproblemthatariseswhentheIRRmethodisusedtoevaluatemutuallyexclusiveinvestments.BecausetheIRRisapercentage,theprocessofcomputationeliminatessize;yet,sizeoftheinvestmentisimportant.TimingAssumethattherearetwomutuallyexclusiveinvestmentsbothrequiringthesameinitialoutlay.Thiscaseseemstobedifferentfromtheonewehavejustdiscussedbecausethereisnoincrementalinvestment.Actually,thedifferenceissuperficial.ConsiderinvestmentsYandZ,describedinTable2.SupposethatYandZaremutuallyexclusiveinvestmentsforacompanywhosecostofmoneyis5%.TheIRRofYis20%,whereasthatofZis25%.I